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                数据结构--堆栈
              
            
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        <p>堆栈是一种特殊的线性表，堆栈的数据元素以及数据元素间的逻辑关系和线性表完成相同的，差别是：线性表可以在任何位置插入删除数据，而堆栈只允许在固定的一端进行插入和删除数据元素操作。</p>
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<p>堆栈的顺序表示与实现保存在<code>SeqStack.h</code></p>
<figure class="highlight c"><table><tr><td class="code"><pre><div class="line"><span class="comment">//顺序堆栈的结构体</span></div><div class="line"><span class="keyword">typedef</span> <span class="keyword">struct</span></div><div class="line">&#123;</div><div class="line">    DataType <span class="built_in">stack</span>[MaxStackSize];</div><div class="line">    <span class="keyword">int</span> top;</div><div class="line">&#125; SeqStack;</div><div class="line"><span class="function"><span class="keyword">void</span> <span class="title">StackInitiate</span><span class="params">(SeqStack *S)</span></span></div><div class="line">&#123;</div><div class="line">    S-&gt;top = <span class="number">0</span>;</div><div class="line">&#125;</div><div class="line"><span class="function"><span class="keyword">int</span> <span class="title">StackNotEmpty</span><span class="params">(SeqStack S)</span></span></div><div class="line">&#123;</div><div class="line">    <span class="keyword">if</span>(S.top &lt;= <span class="number">0</span> ) <span class="keyword">return</span> <span class="number">0</span>;</div><div class="line">    <span class="keyword">else</span> <span class="keyword">return</span> <span class="number">1</span>;</div><div class="line">&#125;</div><div class="line"><span class="function"><span class="keyword">int</span> <span class="title">StachPush</span><span class="params">(SeqStack *S, DataType x)</span></span></div><div class="line">&#123;</div><div class="line">    <span class="keyword">if</span>(S-&gt;top &gt;= MaxStackSize)</div><div class="line">    &#123;</div><div class="line">        <span class="built_in">printf</span>(<span class="string">"堆栈已满\n"</span>);</div><div class="line">        <span class="keyword">return</span> <span class="number">0</span>;</div><div class="line">    &#125;</div><div class="line">    <span class="keyword">else</span></div><div class="line">    &#123;</div><div class="line">        S-&gt;<span class="built_in">stack</span>[S-&gt;top] = x;</div><div class="line">        S-&gt;top ++;</div><div class="line">        <span class="keyword">return</span> <span class="number">1</span>;</div><div class="line">    &#125;</div><div class="line">&#125;</div><div class="line"><span class="function"><span class="keyword">int</span> <span class="title">StackPop</span><span class="params">(SeqStack *S, DataType *d)</span></span></div><div class="line">&#123;</div><div class="line">    <span class="keyword">if</span>(S-&gt;top &lt;= <span class="number">0</span>)</div><div class="line">    &#123;</div><div class="line">        <span class="built_in">printf</span>(<span class="string">"堆栈已空\n"</span>);</div><div class="line">        <span class="keyword">return</span> <span class="number">0</span>;</div><div class="line">    &#125;</div><div class="line">    <span class="keyword">else</span></div><div class="line">    &#123;</div><div class="line">        S-&gt;top--;</div><div class="line">        *d = S-&gt;<span class="built_in">stack</span>[S-&gt;top];</div><div class="line">        <span class="keyword">return</span> <span class="number">1</span>;</div><div class="line">    &#125;</div><div class="line">&#125;</div><div class="line"><span class="function"><span class="keyword">int</span> <span class="title">StackTop</span><span class="params">(SeqStack S, DataType *d)</span></span></div><div class="line">&#123;</div><div class="line">    <span class="keyword">if</span>(S.top &lt;= <span class="number">0</span>)</div><div class="line">    &#123;</div><div class="line">        <span class="built_in">printf</span>(<span class="string">"堆栈已空\n"</span>);</div><div class="line">        <span class="keyword">return</span> <span class="number">0</span>;</div><div class="line">    &#125;</div><div class="line">    <span class="keyword">else</span></div><div class="line">    &#123;</div><div class="line">        *d = S.<span class="built_in">stack</span>[S.top - <span class="number">1</span>];</div><div class="line">        <span class="keyword">return</span> <span class="number">1</span>;</div><div class="line">    &#125;</div><div class="line">&#125;</div></pre></td></tr></table></figure>
<p>顺序堆栈的测试 <code>SeqStackMain.c</code></p>
<figure class="highlight c"><table><tr><td class="code"><pre><div class="line"><span class="meta">#<span class="meta-keyword">include</span> <span class="meta-string">&lt;stdio.h&gt;</span></span></div><div class="line"><span class="meta">#<span class="meta-keyword">define</span> MaxStackSize 20</span></div><div class="line"><span class="keyword">typedef</span> <span class="keyword">int</span> DataType;</div><div class="line"><span class="meta">#<span class="meta-keyword">include</span> <span class="meta-string">"SeqStack.h"</span></span></div><div class="line"><span class="function"><span class="keyword">int</span> <span class="title">main</span><span class="params">(<span class="keyword">void</span>)</span></span></div><div class="line">&#123;</div><div class="line">	SeqStack myStack;</div><div class="line">	<span class="keyword">int</span> i,x;</div><div class="line">	StackInitiate(&amp;myStack);</div><div class="line">	<span class="keyword">for</span>(i=<span class="number">0</span>;i&lt;<span class="number">10</span>;i++)</div><div class="line">	&#123;</div><div class="line">		StachPush(&amp;myStack,i+<span class="number">1</span>);</div><div class="line">	&#125;</div><div class="line">	StackTop(myStack,&amp;x);</div><div class="line">	<span class="built_in">printf</span>(<span class="string">"当前栈顶的元素是：%d\n"</span>, x);</div><div class="line">	<span class="built_in">printf</span>(<span class="string">"依次出栈的顺序为：\n"</span>);</div><div class="line">	<span class="keyword">while</span>(StackNotEmpty(myStack))</div><div class="line">	&#123;</div><div class="line">		StackPop(&amp;myStack,&amp;x);</div><div class="line">		<span class="built_in">printf</span>(<span class="string">"%d   "</span>, x);</div><div class="line">	&#125;</div><div class="line">	<span class="keyword">return</span> <span class="number">0</span>;</div><div class="line">&#125;</div><div class="line"><span class="comment">//结果：当前栈顶的元素是：10</span></div><div class="line"><span class="comment">//依次出栈的顺序为：</span></div><div class="line"><span class="comment">//10   9   8   7   6   5   4   3   2   1</span></div></pre></td></tr></table></figure>
<p>链式堆栈的实现<code>LinStack.h</code></p>
<figure class="highlight c"><table><tr><td class="code"><pre><div class="line"><span class="comment">//LinStack.h</span></div><div class="line"><span class="keyword">typedef</span> <span class="keyword">struct</span> snode</div><div class="line">&#123;</div><div class="line">    DataType data;</div><div class="line">    <span class="keyword">struct</span> snode *next;</div><div class="line"></div><div class="line">&#125; LSnode;</div><div class="line"><span class="comment">//初始化带有头节点的堆栈</span></div><div class="line"><span class="function"><span class="keyword">void</span> <span class="title">StackInitiate</span><span class="params">(LSnode **head)</span></span></div><div class="line">&#123;</div><div class="line">    *head = (LSnode *)<span class="built_in">malloc</span>(<span class="keyword">sizeof</span>(LSnode));</div><div class="line">    (*head)-&gt;next = <span class="literal">NULL</span>;</div><div class="line">&#125;</div><div class="line"><span class="function"><span class="keyword">int</span> <span class="title">StackNotEmpty</span><span class="params">(LSnode *head)</span></span></div><div class="line">&#123;</div><div class="line">    <span class="keyword">if</span>(head-&gt;next == <span class="literal">NULL</span>) <span class="keyword">return</span> <span class="number">0</span>;</div><div class="line">    <span class="keyword">else</span> <span class="keyword">return</span> <span class="number">1</span>;</div><div class="line">&#125;</div><div class="line"><span class="comment">//入栈</span></div><div class="line"><span class="function"><span class="keyword">void</span> <span class="title">StackPush</span><span class="params">(LSnode *head, DataType x)</span></span></div><div class="line">&#123;</div><div class="line">    LSnode *p;</div><div class="line">    p = (LSnode *)<span class="built_in">malloc</span>(<span class="keyword">sizeof</span>(LSnode));</div><div class="line">    p-&gt;data = x;</div><div class="line">    p-&gt;next = head-&gt;next;  <span class="comment">//新节点入栈</span></div><div class="line">    head-&gt;next = p;  <span class="comment">//新节点成为栈顶</span></div><div class="line">&#125;</div><div class="line"><span class="comment">//出栈</span></div><div class="line"><span class="function"><span class="keyword">int</span> <span class="title">StackPop</span><span class="params">(LSnode *head, DataType *d)</span></span></div><div class="line">&#123;</div><div class="line">    LSnode *p = head-&gt;next;</div><div class="line">    <span class="keyword">if</span>(p == <span class="literal">NULL</span>)</div><div class="line">    &#123;</div><div class="line">        <span class="built_in">printf</span>(<span class="string">"堆栈已空\n"</span>);</div><div class="line">        <span class="keyword">return</span> <span class="number">0</span>;</div><div class="line">    &#125;</div><div class="line">    head-&gt;next = p-&gt;next;  <span class="comment">//删除原栈顶元素</span></div><div class="line">    *d = p-&gt;data;</div><div class="line">    <span class="built_in">free</span>(p);</div><div class="line">    <span class="keyword">return</span> <span class="number">1</span>;</div><div class="line">&#125;</div><div class="line"><span class="comment">//取栈顶元素</span></div><div class="line"><span class="function"><span class="keyword">int</span> <span class="title">StackTop</span><span class="params">(LSnode *head, DataType *d)</span></span></div><div class="line">&#123;</div><div class="line">    LSnode *p = head-&gt;next;</div><div class="line">    <span class="keyword">if</span>(p == <span class="literal">NULL</span>)</div><div class="line">    &#123;</div><div class="line">        <span class="built_in">printf</span>(<span class="string">"堆栈已空\n"</span>);</div><div class="line">        <span class="keyword">return</span> <span class="number">0</span>;</div><div class="line">    &#125;</div><div class="line">    <span class="keyword">else</span></div><div class="line">    &#123;</div><div class="line">        *d = p-&gt;data;</div><div class="line">        <span class="keyword">return</span> <span class="number">1</span>;</div><div class="line">    &#125;</div><div class="line">&#125;</div><div class="line"><span class="comment">//撤销动态申请的空间</span></div><div class="line"><span class="function"><span class="keyword">void</span> <span class="title">Destroy</span><span class="params">(LSnode **head)</span></span></div><div class="line">&#123;</div><div class="line">    LSnode *p , *p1;</div><div class="line">    p = head;</div><div class="line">    <span class="keyword">while</span>(p != <span class="literal">NULL</span>)</div><div class="line">    &#123;</div><div class="line">        p1 = p;</div><div class="line">        p = p-&gt;next;</div><div class="line">        <span class="built_in">free</span>(p1);</div><div class="line">    &#125;</div><div class="line">&#125;</div></pre></td></tr></table></figure>
<h3 id="总结"><a href="#总结" class="headerlink" title="总结"></a>总结</h3><p>堆栈是各种软件系统中应用最广泛的数据结构之一，括号匹配和表达式计算是编译软件设计的基本问题，其软件设计中都需要使用堆栈。</p>
<h4 id="表达式计算"><a href="#表达式计算" class="headerlink" title="表达式计算"></a>表达式计算</h4><p>把中缀表达式转变为后缀表达式：</p>
<p>中缀表达式：A+(B-C/D)*E   （这便是我们生活中所熟悉的格式）</p>
<p>后缀表达式：ABCD/-E* </p>
<ul>
<li>后缀算术表达式的操作数与中缀算术表达式的操作数先后次序完成相同，只是运算符的先后次序改变了</li>
<li>后缀算术表达式没有括号，后缀算术表达式的运算符次序就是执行的次序</li>
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